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JAMB Mathematics 2000 Question 19

Question 19

Polynomials

If (x − 1), (x + 1) and (x − 2) are factors of the polynomial ax3 + bx2 + cx − 1, find a, b, c respectively.

  1. A.−½, 1, ½
  2. B.½, 1, ½
  3. C.½, 1, −½
  4. D.½, −1, ½
Show the answer and explanation

Answer: A (−½, 1, ½)

Explanation

The polynomial equals a(x − 1)(x + 1)(x − 2) = a(x3 − 2x2 − x + 2). Matching the constant term, 2a = −1, so a = −½, b = −2a = 1 and c = −a = ½.